Level set method for solving Poisson's equation with
discontinuous nonlinearities

Joseph Kolibal
Abstract:
We study semi-linear elliptic free boundary problems
in which the forcing term is discontinuous;
i.e., a Poisson's equation where the forcing term is
the Heaviside function applied to the unknown minus a constant.
This approach uses level sets to construct a monotonic
sequence of iterates which converge to a class of solutions to the
free boundary problem. The monotonicity of the construction
based on nested sets provides insight into the connectivity of
the free boundary sets associated with the solutions.